Multi-layer associative neural networks (MANN): storage capacity vs. noise-free recall

The author attempts to resolve important issues on artificial neural nets, i.e., exact recall and capacity in multilayer associative memories. The following triple-layered neural network is proposed: the first synapse is a one-shot associative memory using the modified Kohonen´s adaptive learning algorithm with arbitrary input patterns; the second is Kosko´s bidirectional associative memory consisting of orthogonal input/output basis vectors, such as Walsh series, satisfying the strict continuity condition; and the third is a simple one-shot associative memory with arbitrary output images. A mathematical framework based on the relationship between energy local minima and noise-free recall is established. The robust capacity conditions of this multi-layer associative memory are derived, which leads to forming the energy local minima at the exact training pairs. The proposed strategy maximizes the total number of stored images, and completely relaxes any code-dependent conditions of the learning pairs